Corollary 1.2 
When \(n\ge 4\) , then any quasiconformal homeomorphism \(U\rightarrow U^{\prime }\subset  between connected open subsets is the restriction of a diffeomorphism of the form \) g\( for some \) gGL(n,R)\(, \) {0,1}\(.\) 
Since \((N,V_1)\)  is contact diffeomorphic to \((\hat{N},W\mbox{\Large $|$\normalsize }_{\hat{N}})\) , the above results give a classification of Sobolev mappings \(N\supset U\rightarrow N\)  with nondegenerate Pansu differential; this applies in particular quasiconformal homeomorphisms and quasiregular maps by [1]}. Corollary REF  was previously known for real analytic diffeomorphisms [2]}, [3]}, \(C^2\)  diffeomorphisms [4]}, [5]}, and Euclidean bilipschitz homeomorphisms [6]}.
